Our general perturbation formalism1 for the propagation of Rayleigh waves on the surface of initially deformed anisotropic material plates is applied to the problem of separation of material texture and stress. The preferential alignment of crystallographic axes in a polycrystalline material is described in terms of their orientation distribution function2. We consider explicitly the case of an orthotropic distribution of cubic crystallites, which occurs, for example, in aluminum and steel alloys. The measured values of the Rayleigh wave phase velocity at different angles on the material plate can be used for the determination, in a reference plate with similar texture, of the three coefficients W400, W420 and W440, which characterize the orientation distribution. An extension of the formalism then allows us to separate the acoustoelastic effects of the initial stresses. An error analysis and a comparison with similar techniques using grazing SH-waves complete our discussion.